Question

The value of $\underset{x\to \infty }{lim}\frac{2\sqrt{x}+3\sqrt[3]{3x}+5\sqrt[5]{5x}}{\sqrt{3x-2}+\sqrt[3]{32x-3}}$ is -

• A. $\frac{1}{\sqrt{3}}$
• B. $\sqrt{3}$
• C. $\frac{2}{\sqrt{3}}$
• D. $2\sqrt{3}$

Answer 1

Answer: (C)

$\frac{2}{\sqrt{3}}$

$\underset{x\to \infty }{lim}\frac{2\sqrt{x}+3\sqrt[3]{3x}+5\sqrt[5]{5x}}{\sqrt{3x-2}+\sqrt[3]{32x-3}}$
$=\underset{x\to \infty }{lim}\frac{2+3\sqrt[3]{3\frac{1}{x^{1/2}}}+5\sqrt[5]{5\frac{1}{x^{3/2}}}}{\sqrt{3-\frac{2}{x}}+\sqrt[3]{3\frac{2}{x^{1/2}}-\frac{3}{x^{3/2}}}}=\frac{2}{\sqrt{3}}$